MAA American Mathematics Competitions

2018 INVITATIONAL COMPETITIONSTEACHER’S MANUALA guide for administering the AIME, USAMO, and USAJMO

Mathematical Association of AmericaPO Box 471 Annapolis Junction, MD 20701

800-527-3690 • maa.org/amc

COMPETITION DATES: AIME: TUESDAY, MARCH 6, 2018 OR WEDNESDAY, MARCH 21, 2018USAMO & USAJMO: WEDNESDAY, APRIL 18, 2018 AND THURSDAY, APRIL 19, 2018

Introduction to American Invitational Mathematics Exam and USA Mathematical Olympiad

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Invitational Exam Contact Information:For any questions regardingAIME administration, please contact:

Email: amcinfo@maa.org Phone: 800-527-3690

For any questions regardingUSAMO and USAJMO administration, please contact:

Email: usamoinfo@maa.org Phone: 202-417-2048 Fax: 202-379-7852

Email contact is preferred.

WELCOME TO THE 2018 COMPETITION36TH ANNUAL AMERICAN INVITATIONAL MATHEMATICS EXAMAND THE 47TH ANNUAL USA MATHEMATICAL OLYMPIAD

AMERICAN MATHEMATICS COMPETITIONS PROGRAM LEADS THE NATIONIN STRENGTHENING THEMATHEMATICAL CAPABILITIESOF THE NEXT GENERATIONOF PROBLEM-SOLVERS.

What is the MAA American MathematicsCompetitions (AMC) Program? The Mathematical Association of America American Mathematics Competitions program leads the nation in strengthening the mathematical capabilities of the next generation of problem solvers. Through classroom resources and friendly competition, the MAA AMC program helps America’s educators identify talent and foster a love of mathematics. The MAA AMC program positively impacts the analytical skills needed for future careers in an innovative society. The MAA American Mathematics Competitions are a series of examinations and accompanying curriculum materials that develop problem-solving skills and mathematical knowledge in middle and high school students.

What is the American Invitational MathematicsExamination (AIME)?

When is the AIME?The AIME I is administered on Tuesday, March 6, 2018. The AIME II is administered on Wednesday, March 21, 2018. Students who qualified for the AIME will automat-ically be registered to take the AIME I. If a competition manager cannot administer the AIME I and needs to administer the AIME II instead, they must complete the

What are the USAMO and USAJMO? The USA Mathematical Olympiad (USAMO) and the USA Junior Mathematical Olympiad (USAJMO) are both six-question proof-based examinations, that take place 4.5 hours each day for two consecutive days. Students will be invited to take the USAMO based on a combina-tion of their AMC 12 and AIME scores. Students will be invited to take the USAJMO based on a combination of their AMC 10 and AIME scores. U.S. citizens and students studying in the United States and Canada who meet the age and grade requirements are eligible to qualify for the USAMO and USAJMO.

AIME II registration form and pay the associated fees. On competition day, the competition should be adminis-tered between 8:45 a.m. and 12:15 p.m. in the school’s US time zone. For time zones outside of the continental United States, the competition must be given after 9AM, EDT (UTC-4) on the day of the competition.

When are the USAMO and USAJMO?

The AIME is a challenging exam offered to students whoexcelled on the AMC 10 or AMC 12 competition. It is a 15-question, three-hour examination, where each answer is an integer between 0 and 999. The questions on the AIME are more difficult than those on the AMC 10 and AMC 12 competitions.

Day one of the USAMO and USAJMO is Wednesday, April 18, from 12:30 p.m. EDT to 5:00 p.m. EDT. Day two of the USAMO and USAJMO is Thursday, April 19, from 12:30 p.m. EDT to 5:00 p.m. EDT. Three questions are given each day, and participants are expected to com-pete on both days.

Pre-Competition Preparation: AIME

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Administering the AIME: What You Need To KnowUse these checklists to host a successful AIME competition.

Pre-competition checklist for AIME:

• Please review all answer sheets to ensure that theyhave been marked correctly.

• Review the complete set of competition rules.

• Confirm the time and location of the competition with all of your students who qualified.

• Locate the AIME materials that were mailed to you with your AMC 10/12 materials. Instruct your student(s) who qualified for the AIME to complete side 1 of the AIME student answer sheet using the instructions located on the top left corner of the answer sheet. Carefully follow the marking instruc-tions on both the student answer sheet.

• Students must use their full legal name, no nick-names or abbreviations. They should pay careful attention to marking their name accurately. Their name on the AIME answer sheet must match the name they used to complete the AMC 10/12 answer sheet. Once student information has been submitted, the MAA AMC program office can not edit any of the information provided on the answer sheet.

• Reserve a quiet room for at least 3 hours and 30 minutes on the day of the competition, from 8:45 a.m. to 12:15 p.m. in your school’s U.S. time zone, to allow time for pre- and post-competition activities. For time zones located outside of the continental United States, the competition must be given after 9:00 a.m., EDT (UTC-4) on the competition day. In extreme cases, when you cannot administer the AIME between 7:00 a.m. and 3:00 p.m., please complete the academ-ic integrity form.

• Complete the School Identification Form and USAMO/USAJMO Identification Form using the instructions found on those forms.

• Make arrangements to mail the AIME return enve-lopes with a mail service that offers package tracking. FedEx or UPS are strongly recommended.

• Obtain a supply of #2 pencils and unmarked scratch paper. Inform students that no aids are permitted other than scratch paper, graph paper, rulers, protractors, and erasers. NO CALCULATORS OR ELECTRONIC DEVICES OF ANY KIND ARE ALLOWED. No AIME questions require the use of a calculator.

How do you prepare students for the AIME? The AIME has a different format than the AMC 10 and AMC12. The competition is three hours, all answers are three-digit integers, and there are 15 problems. If you havestudents who are first-time AIME qualifiers, show them the MAA AMC Invitational Competitions webpage so that they can familiarize themselves with the types of problems on the AIME.

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AIME Venue Policy:Students must take the AIME at the same testing location where they took the AMC 10 or AMC 12. This is to ensure that a student’s AMC 10 or AMC 12 score can be accurately matched with their AIME score for USAMO and USAJMO qualification. In the event that a student absolutely cannot take the AIME at the same competition location, they are to make arrangements with a different competition manager who already has the materials to proctor the exam. The new proctor is to complete the Change of Venue form available on the MAA AMC Invitational Competitions webpage. Students seeking a new venue for AIME participation should reach out to nearby schools, using the Additional Competition Locations tool to look up other AIME host sites nearby. The MAA AMC program will only accommodate change of venue arrangements that have been made between a student and an approved proctor.

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How do students qualify to participate in the AIME?Qualification parameters for the AIME vary each competition cycle. For the AMC 10, at least the top 2.5% of all sco ers on the AMC 10A and the top 2.5% of scorers on the AMC 10B are invited to take the AIME. For the AMC 12, at least the top 5% of all scorers on the AMC 12A and the top 5% of scorers on the AMC 12B are invited. The cutoff scores for AIME qualification will be announced after each competition (10A, 10B, 12A, and 12B) based on the distribution of scores. There is no predetermined cutoff score for the 2018 AIME, and this year’s AIME cutoff may differ from last year’s.

AIME Administration Policy:The AIME I must be administered on March 6, 2018, and theAIME II must be administered on March 21, 2018 to all students who qualified. Students who qualified for the AIME may take either the AIME I or AIME II. They may not take both. Any student that takes both the AIME I and AIME II will be disqualified. The competition must be administered at the same time and location on both days. The AIME I and AIME II consist of different questions but are of equal difficulty. If you have a student that qualified for the AIME but is unable to take the AIME I, please register for the AIME II. To do this, you can complete an AIME II Registration Form and email it to amcinfo@maa.org. Please note that there is a processing fee for the AIME II.

AIME Competition

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Competition Delivery:

Administering the AIME: What You Need To Know Use these checklists to host a successful AIME competition.

Before the competition

• Seat students so they are separated by an empty space, if possible.

• Hand out the printed AIME questions and inform students that they are not to open the packet containing the questions until they are instructed to do so.

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• When it is time to begin, tell students to open the packet containing the AIME questions and to be careful to match their answers to the correspondingquestion. Remind students that there are 15 problemsand that they have three hours to complete the competition. Then tell them to BEGIN.

During the exam

• Ensure that you have printed enough copies of the AIME questions for each of your AIME qualifiers.

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• Read aloud the following instructions:

• For each question, use a #2 pencil to write your answer at the top of the problem’s answer column. Use 3 digits: each problem has only one correct answer, which is an integer between 000 and 999, inclusive. Then, in each of these columns, bubble in the one circle which is labeled with the digit you have written at the top.

• DO NOT BUBBLE IN ANSWERS UNTIL YOU ARE CERTAIN OF YOUR FINAL CHOICE. Answer sheets that contain stray marks may not be read correctly by the scanner that scores the competi-tion.

• Return the previously completed AIME answer sheets to the correct students and provide them with a #2 lead pencil with an eraser.

• Provide as quiet an environment as possible.

• Participants should be continuously monitored by the competition manager during the competition.

• Be sure that no student has access to any electronic devices, including calculators and cellphones, during the competition.

• Warn any student whose eyes wander, and disqualify any students that are clearly copying or collaborating.

• If there is an urgent need to use the bathroom, only one student may leave at a time and their answer sheet and the AIME questions packet should remain with the competition manager while the student is out of the room. If there is a health or medical emergency, a backup competition manager should be available to assist in adminstering the competition.

• Make an announcement when there are 90 minutes left and again when there are 15 minutes left.

• When time is up after three hours, tell the students to STOP and have them sign their name in the space provided in the middle of side 2 of the student answer sheet.

• Collect the answer sheets and AIME question packets immediately following the administration of the compe-tition. Once all answer sheets are received, check that each student’s name is correct and that the answer sheet is bubbled in correctly.

• Inform the students that the competition and solutions may not be discussed with anyone outside of the room either orally or digitally (e.g. email, online, and social media of any type) until 24 hours have passed from the official competition date. The AIME questions must be collected from the students immediately after the competition, but they may be returned 24 hours after the competition period is over.

An email will be sent to the inbox of the email address that you used to register for the AMC 10 or AMC 12 com-petition on Monday, March 5, 2018 at 1:00 p.m. EDT for the AIME I and on Tuesday, March 20, 2018 at 1:00 p.m. EDT for the AIME II. This email will contain a link to a password protected PDF of the AIME questions. Print the out the PDF of the AIME questions and make enough copies for each of your AIME qualifiers. To ensure that you are able to receive this email, please add amcin-fo@maa.org to your list of approved contacts.

Ask if there are any questions about competition procedures. Inform students that talking or asking questions during the competition is not allowed. They must do their own work.

Instruct students to read the entire front cover of the AIME question packet. Allow 5 minutes for students to review the front cover.

AIME Competition

A er the competition AIME Reports:

USAMO & USAJMO Quali cation Announcements:

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• Please do not score the answer sheets. Send them to the MAA AMC office in Annapolis Junction, MD for scoring.

• Check student answer sheets for complete personal information (legal name, date of birth, gender, etc.).

• Arrange the answer sheets so that each sheet faces the same direction with the same side up. Remove all paper clips, rubber bands, and note paper attached to the answer sheets. Make sure that no two sheets are stuck together.

• After you have mailed all of the answer sheets, you may discuss the competition and solutions with your students. Remember that there will be schools taking the competition at different times. It is important that no one discusses the problems and solutions in any online or public forum.

• Place the School Identification Form on top of the answer sheets and insert all sheets in the return envelope.

• Complete the AIME Certification Form and USAMO/USAJMO Identification Form. Make sure that your principal or person with comparable title signs the certification form where it is indicated and that you complete the rest of the form.

Seal the envelope and indicate the number of answer sheets that you are returning in the space provided on the front of the return envelope.

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• Ship with appropriate postage using a trackable method. FedEx or UPS are strongly recommended. The MAA AMC is not responsible for lost or delayed answer sheets.

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• The AIME student answer sheets sent to the MAA AMC office in Annapolis Junction, MD for scoring will not be returned to competition managers.

• The MAA AMC office makes all possible attempts to contact qualifiers and competition managers about USAMO and USAJMO qualification:

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• Competition managers will be emailed a list of students who took the AIME at their school which will indicate any students who qualified for the USAMO or the USAJMO. It will also include their USAMO or USAJMO student ID numbers which they will need for all USAMO or USAJMO paperwork.

• If the MAA AMC office has been given a legible student email on the AIME answer sheet, they will also email these students individually to let them know they have qualified and provide them with their USAMO or USAJMO ID number.

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• Place the certification form in the AIME return enve-lope with the answer sheets, School Identification Form, and USAMO/USAJMO Identification Form.

AIME scores, PDF certificates of participation, and the AIME solutions guide, will be emailed to competition managers after the competition has been scored. Please retain the score report for future reference. Many students cite their scores on applications to college and other programs. The MAA AMC office cannot look up individual student scores after the com-petition cycle has ended.

A list of USAMO and USAJMO qualifiers will be posted on the MAA AMC website on Tuesday, April 3, 2018. This list will provide the first initial, last name, school, city, state, and grade of each qualifier.

Some students may appear on this list that had scores below the USAMO and USAJMO cutoff indexes. In certain cases, the USAMO committee invites students from underrepresented states to take part in the competition. Please check this list even if none of your students scored above the USAMO or USAJMO cutoff indexes.

Cutoff indexes will be announced on the MAA AMC website on Tuesday, April 3, 2018. If you discover that you have a student with a score above the cutoff who did not receive a student ID number for the USAMO or USAJMO, or was not listed as a qualifier, please contact usamoinfo@maa.org to see if there was an error in matching the student’s AIME score with their AMC 10 or AMC 12 scores.

March 19, 2018 is that last day that AIME I answer sheets will be accepted by the MAA AMC office for scoring. March 28, 2018 is the last day that AIME II answer sheets will be accepted.

Pre-Exam Preparation: USAMO and USAJMO

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Administering the USAMO & USAJMO - What You Need To Know Use these checklists to host a successful competition.

Pre-competition checklist for USAMO & USAJMO:

How do students qualify to participatein the USAMO or USAJMO?

How do you prepare students for the USAMO?The format of the USAMO and USAJMO is identical to the format of the International Mathematical Olympiad. Both the USAMO and USAJMO consist of six proof-based questions to be solved over two days. Tthree questions will be given on Wednesday, and three questions will be given on Thursday. Each day, students will have 4 hours and 30 minutes to solve them. Student answers will be graded based on how they approached the problem, clarity of reasoning, evidence of ingenuity, inventiveness, and general insight. Please make sure students have read the USAMO/USAJMO Instruction Sheet, and have read our MAA AMC Invitational Compe-titions webpage to prepare for the competition.

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• Either parents, students, or competition managers must complete and submit the 2018 Student/Parent Response Form. The form must be scanned and emailed to usamoinfo@maa.org. The deadline for returning this form is Friday, April 13, 2018.

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• Review the competition distribution instructions that were sent to you via email along with your list of student qualifiers. If you have not received any instructions or a list of qualifiers, and will have students sitting for the competition, email usamoinfo@maa.org as soon as possible.

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• Complete the 2018 USAMO/USAJMO Teacher Acknowledgement Form, scan the completed form and email it to usamoinfo@maa.org. The deadline for returning this form is Friday, April 13, 2018.

After the AIME I and AIME II are scored, the USAMO committee and MAA AMC program will determine the cutoff indexes that will qualify students for USAMO or USAJMO participation. Each year the MAA AMC program selects approximately 500 students total for the two Olympiads. The USAMO and USAJMO indexes are calculated as follows:

USAMO Index = AMC 12 Score + 10 × AIME Score

USAJMO Index = AMC 10 Score + 10 × AIME Score

When determining the cutoff index, the USAMO com-mittee considers the difference in difficulty of the AMC 10/12 A and B competitions, as well as the difference in difficulty in the AIME I and AIME II, as determined by score distribution. If this difference is significant, differ-ent cutoffs may be announced for the different compe-titions. If a student’s scores qualify them for both the USAMO and the USAJMO, they will be invited to take the USAMO. The USAMO committee may choose to invite additional students to take the USAMO or USAJMO. For example, the committee may invite the top scoring students from underrepresented states to take the competition. Only students who are U.S. citizens or are attending school in the United States or Canada are eligible to participate in the USAMO and USAJMO.

Reserve a room for April 18, 2018 and April 19, 2018 from 12:00 p.m. EDT to 5:30 p.m. EDT on both days to allow for pre- and post-competition activities. The competition must begin at 12:30 p.m. EDT and end at 5:00 p.m. EDT.

If you cannot administer the competition for the entire time on both competition dates, please find another competition manager to assist you. Students must be supervised contin-uously for the duration of the competition period on both days. When submitting any sheets, provide names and contact information for anyone who helped proctor.

Confirm with participating students that they know their ID number, the date and location of the competi-tion, and that they plan on participating in the competition. Tell all students to arrive to the room by 12:15 p.m. EDT on the day of the competition The competition must begin at 12:30 p.m. EDT, and students cannot be given any additional time past 5:00 p.m. EDT.

USAMO and USAJMO problems will be distrib-uted via email to competition managers with students who qualified. The email will contain a link to a password-protected PDF of USAMO and USAJMO problems as well as the password for accessing those files.

USAMO and USAJMO Competition

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Before the competition:

• At 12:30 p.m. EDT, tell the students to BEGIN.

During the competition:

Administering the USAMO and USAJMO - What You Need To Know Use these checklists to host a successful competition.

WHEN STUDENTS ARRIVE IN THE CLASSROOM,ASK THEM TO PUT AWAY ALL ELECTRONIC DEVICES.

• Students should come prepared with lunch and/or snacks since there will be no lunch break during the competition. Make sure that the room has enough working space for students and that students will be free from interruptions.

• Before the students arrive, print out plenty of blank USAMO/USAJMO answer sheets. There will be three questions each competition day. Students may require several answer sheets for each of these proof-based questions.

• When students arrive to the classroom, ask them to put away all electronic devices. The only materials they may access while they are in the exam room are a ruler, scratch paper, pencil and eraser.

• At 12:15 p.m. EDT on day one and day two of the USAMO and USAJMO, the competition questions will be emailed to competition managers. If by 12:17 p.m. EDT you have not received the questions, email usamoinfo@maa.org.

• Print enough copies of the competition questions for each of your students. Please be sure to print copies of the USAMO for all USAMO qualifiers, and to print copies of the USAJMO for all USAJMO qualifiers. If your student takes the wrong version of the competition, they will not be given credit for their work.

• Before handing out the competition questions, read the USAMO/USAJMO Instruction Sheet to students.

• Hand out the competition questions face down to each student, again making sure that USAMO quali-fiers receive the USAMO, and USAJMO qualifiers receive the USAJMO.

• If there is an urgent need to use the bathroom, only one student may leave at a time and their answer sheet and questions should remain with the competi-tion manager while the student is out of the room. If there is a health or medical emergency, a backup competition manager should be available to assist with administration.

• Make an announcement when there are 3 hours left, 2 hours left, 1 hour left, and 5 minutes left.

• When time is up at 5:00 p.m. EDT, tell the students to STOP. Check that they have included the correct problem number and page number on all of their answer sheets, as well as their USAMO or USAJMO student ID number on every page.

• Collect all the students’ competition questions and answer sheets following the administration of the competition.

Participants should be continuously monitored by the competition manager during the competition.

•Provide as quiet an environment as possible.•

Warn any student whose eyes wander, and disqualify any students that are clearly copying or collaborating.

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Be sure that no student has access to any electronic devices, including calculators and cellphones, during the competition.

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These instructions are for both day one and day two of the USAMO and USAJMO.

Inform the students that the competition and solutions may not be discussed with anyone either orally or digitally (e.g. email, online, and social media of any type) until at least 7 p.m. EDT, on the day of the competition. The competition questions must be collected from the students immediately after the competition, but they may be returned 24 hours after the competition period is over.

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USAMO & USAJMO Competitions

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A er the competition:Please note that these instructions are for both dayone and day two of the USAMO and USAJMO.

• DO NOT MAIL IN ANY ANSWER SHEETS TO THE AMC OFFICE.

• Complete the USAMO/USAJMO Certification Form for each day of the competition and make sure that your principal or person with comparable title signs the certification form where it is indicated and that you complete the rest of the form.

Mathematical Olympiad Program (MOP):The MOP is an invitational summer program for the US International Mathematical Olympiad (IMO) team and top scoring USAMO and USAJMO students. These students are invited to enter a further series of Olympi-ad-style tests that will determine the following year's IMO team.

• When emailing the form and student answer sheets, use the subject line: Answer Sheets - Day (1 or 2), ID # (List all student IDs).

• If multiple students participated, attach each student’s answer sheets as separate files. For example, if two students took the competition, email two PDFs, one for each student.

USAMO & USAJMO Grading:

USAMO Winners:The 12 top-scoring students on the USAMO will be invit-ed to attend an award ceremony held in Washington, D.C. on June 4, 2018. Activities will include a reception at the Mathematical Association of America headquar-ters and a celebration dinner with the mathematical sciences community. These 12 students will be emailed May 11, 2018, with details about the awards ceremony. The names and schools of winners will also be announced online.

• As soon as possible, scan and email the certification form and answer sheets to usamoinfo@maa.org.

• The MAA AMC office will check every certifi-cation form and every answer sheet to make sure that they are complete and legible. Due to the large volume of responses, it may take up to 48 hours to confirm receipt of all answer sheets. It may take an additional week to confirm that every page of every answer sheet is legible enough for grading. For this reason, we ask that competition managers keep student answer sheets for at least seven days after the second day of the competition.

Each paper is read by as many as four different graders, who agree on a score between 0 and 7 for each ques-tion. Every paper is scored using the same rubric as every other paper. If a student’s score is close to being eligible for an award or Mathematical Olympiad Program (MOP) qualification, their answer sheets will be subject to further review by the graders. Scores will be posted on maa.org/amc on May 11, 2018 by student ID number. All competition managers will be emailed their students’ scores that day. Students will also receive an email with their total score. Scores for individual ques-tions are not available. All scores are final.

The Mathematical Olympiad Program will take place June 3 – June 27, 2018, on the campus of Carnegie Mellon University. Students will take classes on advanced mathematical topics, meet special guest speakers, train for mathematical competitions, and participate in social and mathematical activities. Students who are invited to MOP will receive an email on May 11, 2018, with details about the program.

AMC Policies

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GOOD LUCK TOYOUR STUDENTSON THE 2018 AIME,

USAMO & USAJMO!We hope they find the competitionschallenging, fun,and exciting.

Policy for ChangesThe MAA Committee on the American Mathematics Competitions may change the program rules, regula-tions, awards and conditions of participation in whole or in part. Whenever possible, competition managers will be notified of these changes ahead of time.

Questionable Scores

Early AdministrationEarly administration is NEVER permitted and will result in the disqualification of all the results at your school. Early administration jeopardizes the validity of all scores from other schools.

The only official days for the AIME are March 6 for the AIME I and March 21 for the AIME II. The only official days for the USAMO and USAJMO are April 20 and April 19 from 12:30 p.m. EDT to 5:00 p.m. EDT. Only official AIME participants are eligible to qualify for the USAMO or USAJMO, and only the answer sheets from official USAMO and USAJMO participants will be scored. If the AIME is administered in a time zone outside of the conti-nental United States, the competition must begin after 9:00 a.m. EDT on the official competition day.

Competition Administration• The AIME, the USAMO, and USAJMO must be admin-

istered by a competition manager. This person is a teacher, school administrator or coach and must be a responsible adult who not related to any of the participants. Under no circumstances may a parent administer any competition.

• The proctoring of the competition must take place in a public building (e.g., schools, universities, or places of worship).

• All students must take the competition at the same time under the supervision of a competition manag-er who fully understands the responsibilities and is not related to any of the students.

Students with Accommodation PlansIf a student who qualified for the AIME is visually impaired and/or has a learning disability, contact the MAA AMC office at amcinfo@maa.org to discuss accom-modations. The time allowance for students with learn-ing disabilities is 4 hours and 30 minutes. If a student who qualified for the USAMO or USAJMO is visually impaired and/or has a learning disability, contact the USAMO office at usamoinfo@maa.org.

If it is clear to the competition manager from personal observation that a student has cheated, then the competition manager must disqualify that student. If the competition manager receives an accusation or obtains indirect evidence of cheating, then the competition manager must hold back the student’s answer sheets and immediately report all the facts of the situation to the MAA AMC Office at amchq@maa.org. The AMC Director, in conjunction with the MAA Committee on the American Mathematics Competitions, will determine what to do. UNDER NO CIRCUMSTANCES may the school decide on its own to accept a questionable score.